1/2x+1/3=1/5x

Solution for 1/2x+1/3=1/5x equation:

1/2x+1/3=1/5x

We move all terms to the left:

1/2x+1/3-(1/5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+1/5x)+1/3=0

We get rid of parentheses

1/2x-1/5x+1/3=0

We calculate fractions


50x^2/90x^2+45x/90x^2+(-18x)/90x^2=0

We multiply all the terms by the denominator


50x^2+45x+(-18x)=0

We get rid of parentheses

50x^2+45x-18x=0

We add all the numbers together, and all the variables

50x^2+27x=0

a = 50; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·50·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*50}=\frac{-54}{100}
=-27/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*50}=\frac{0}{100}
=0
$